• Korean Journal of Mathematics
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• 제13권1호
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• pp.19-34
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• 2005

Pricing and hedging strategy for European options of jump-type asset models, which are derived from a stochastic differential equations, are discussed.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.293-310
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• 2007

Recently a risk measure pricing and hedging is replacing a utility-based maximization problem in the literature. In this paper, we treat the optimal problem of risk measure pricing and hedging in the friction market, i.e. in the presence of transaction costs. The risk measure pricing is also verified with the contexts in the literature.

• 대한수학회지
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• 제41권3호
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• pp.513-533
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• 2004

We present the pricing and hedging method for options with general payoffs in the presence of transaction costs. The convexity of the payoff function-gamma of the options- is an important issue under transaction costs. When the payoff function is convex, Leland-style pricing and hedging method still works. However, if the payoff function is of general form, additional assumptions on the size of transaction costs or of the hedging interval are needed. We do not assume that the payoff is convex as in Leland 〔11〕 and the value of the Leland number is less (bigger) than 1 as in Hoggard et al. 〔10〕, Avellaneda and Paras 〔1〕. We focus on generally recognized asymmetry between the option sellers and buyers. We decompose an option with general payoff into difference of two options each of which has a convex payoff. This method is consistent with a scheme of separating out the seller's and buyer's position of an option. In this paper, we first present a simple linear valuation method of general payoff options, and also propose in the last section more efficient hedging scheme which costs less to hedge options.

• 대한수학회보
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• 제56권5호
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• pp.1129-1141
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• 2019

We propose a stochastic delay financial model which describes influences driven by historical events. The underlying is modeled by stochastic delay differential equation (SDDE), and the delay effect is modeled by a stopping time in coefficient functions. While this model makes good economical sense, it is difficult to mathematically deal with this. Therefore, we circumvent this model with similar delay effects but mathematically more tractable, which is by the backward time integration. We derive the option pricing equation and provide the option price and the perfect hedging portfolio.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제4권2호
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• pp.77-84
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• 2000

Black-Scholes equation arising from option pricing in the presence of cost in trading the underlying asset is derived. The transaction cost is chosen precisely and generalized to reflect the trade in the real world. Furthermore the concept of the bandwidth is introduced to obtain the better rehedging. The model with bandwidth derived in this paper can be used to calculate the more accurate option price numerically even if it is nonlinear and more complicated than the models shown before.

• 재무관리연구
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• 제26권3호
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• pp.227-246
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• 2009

옵션 모형에 관한 실증연구에서 모형의 적격성을 평가하는데 사용한 잣대는 옵션 모형으로 구한 이론적 가격과 시장옵션가격간의 가격괴리를 평가하거나 일정기간동안 정기적으로 재조정한 헤지포트폴리오의 성과를 비교하는 것이다. 기존의 연구에서는 기초자산의 변동성에 대한 Black-Scholes 모형의 엄격한 가정을 이완시킨 확률적 변동성 모형이 Black-Scholes 모형의 가격괴리를 크게 개선하고 있음을 밝히고 있으나 동태적 헤지성과에 대해서는 여러 연구가 일관된 결과를 도출하고 있지 못하고 있다. 이 연구에서는 시뮬레이션 기법을 이용하여 Heston의 확률적 변동성 모형의 가정이 완벽히 구현되는 상황을 재현하고 그 상황에서 Heston 모형과 Black-Schols 모형의 동태적 헤지성과를 비교하였다. 시뮬레이션 결과에 따르면 헤지수단으로 기초자산만을 사용하였을 경우 완전히 적격한 모형인 Heston 모형은 확률적 변동성을 감안하지 않은 Black-Scholes 모형에 비해 헤지위험을 크게 줄이지 못하는 것으로 나타났다. 이 결과는 동태적 헤지성과로 옵션모형의 적격성을 평가하는 데는 일정부문 한계가 있을 수 있다는 점을 시사한다. 한편 실무적인 측면에서 옵션거래에 대한 동태적 헤지수단으로 굳이 확률적 변동성 모형과 같은 복잡한 모형을 이용할 필요가 없다는 점을 내포한다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제15권1호
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• pp.1-17
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• 2011

A new method for option pricing based on the trinomial tree method is introduced. The new method calculates the local average of option prices around a node at each time, instead of computing prices at each node of the trinomial tree. Local averaging has a smoothing effect to reduce oscillations of the tree method and to speed up the convergence. The option price and the hedging parameters are then obtained by the compact scheme and the Richardson extrapolation. Computational results for the valuation of European and American vanilla and barrier options show superiority of the proposed scheme to several existing tree methods.

• Industrial Engineering and Management Systems
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• 제10권2호
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• pp.170-177
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• 2011

We present an improved binomial method for pricing financial deriva-tives by using cell averages. After non-overlapping cells are introduced around each node in the binomial tree, the proposed method calculates cell averages of payoffs at expiry and then performs the backward valuation process. The price of the derivative and its hedging parameters such as Greeks on the valuation date are then computed using the compact scheme and Richardson extrapolation. The simulation results for European and American barrier options show that the pro-posed method gives much more accurate price and Greeks than other recent lattice methods with less computational effort.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권4호
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• pp.287-298
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• 2013

A standard deviation has been a starting point for a mathematical definition of risk. As a remedy for drawbacks such as subadditivity property discouraging the diversification, coherent and convex risk measures are introduced in an axiomatic approach. Choquet expectation and g-expectations, which generalize mathematical expectations, are widely used in hedging and pricing contingent claims in incomplete markets. The each risk measure or expectation give rise to its own pricing rules. In this paper we investigate relationships among dynamic risk measures, Choquet expectation and dynamic g-expectations in the framework of the continuous-time asset pricing.

• 전기학회논문지
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• 제60권2호
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• pp.266-272
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• 2011

Real Time Pricing(RTP) is used not only to stabilize the price volatility in electricity market, but to hedge the price risk for Load Serving Entity(LSE). This paper presents an efficient method to reduce the risk of the price volatility in real-time electricity market. For designing the RTP, load patterns of customer are calculated by applying the demand elasticity and customer's utility is also analyzed to compute the RTP revenue through the risk-attribute of the LSE. In the end, the distribution of the LSE's profits can be evaluated to lead the optimal RTP value, depending on the level of customer's participation. Results from the case study based on PJM data are reported to illustrate the proposed method.